Answer
A: c (c-2)/ 2 (c +2)
Step-by-step explanation:
Which is equal to c^2-4c+4/ 12c^3+ 30c^2 divided by c^2-4/ 6c^4 +15c^3?
A: c (c-2)/ 2 (c +2)
B: 2 (c-2)/ c(c+2)
C: 2 (c+2)/ c(c-2)
D: c(c+2)/ 2(c-2)
[c^2 - 4c + 4] / [12×(c^3) + 30×(c^2)] ÷ [c^2 - 4] / [6×(c^4) +15×(c^3)]
Expand the expression
= [c^2 - 2×2×c + 2^2] / [6×(c^2)×(2c + 5)] ÷ [c^2 - 2^2] / [3×(c^3)×(2c +5)]
Factorize the expression
= [(c-2)^2] / [6×(c^2)×(2c + 5)] ÷ [(c-2)(c+2)] / [3×(c^3)×(2c +5)]
Multiply by interchanging the numerator and denominator of the divisor
= [(c-2)^2] / [6×(c^2)(2c + 5)] × [3(c^3)(2c +5)] / [(c-2)(c+2)]
= [(c-2)×3(c^3)] / [6×(c^2)×(c+2)]
= [c×(c-2)] / [2×(c+2)]
= c(c - 2) / 2(c + 2)
[c^2 - 4c + 4] / [12×(c^3) + 30×(c^2)] ÷ [c^2 - 4] / [6×(c^4) +15×(c^3)] = c(c - 2) / 2(c + 2)
Answer:
A: [tex]\frac{c(c-2)}{2(c+2)}[/tex]
Step-by-step explanation:
[tex]\frac{c^{2} -4c+4}{12c^{3} + 30c^{2}}[/tex] ÷ [tex]\frac{c^{2} -4}{6c^{4} + 15c^{3}}[/tex]
expand.
= [c^2 - 2×2×c + 2^2] / [6×(c^2)×(2c + 5)] ÷ [c^2 - 2^2] / [3×(c^3)×(2c +5)]
factorize.
= [(c-2)^2] / [6×(c^2)×(2c + 5)] ÷ [(c-2)(c+2)] / [3×(c^3)×(2c +5)]
multiply by the reciprocal.
= [(c-2)^2] / [6×(c^2)(2c + 5)] × [3(c^3)(2c +5)] / [(c-2)(c+2)]
= [(c-2)×3(c^3)] / [6×(c^2)×(c+2)]
= [c×(c-2)] / [2×(c+2)]
= A: [tex]\frac{c(c-2)}{2(c+2)}[/tex]
